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          <h1 class="post-title" itemprop="name headline">heap堆</h1>
        

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        <p>堆<br><a id="more"></a><br>首先我们先来看看完全二叉树<br>完全二叉树：对于一个树高为h的二叉树，如果其第0层至第h-1层的节点都满。如果最下面一层节点不满，则所有的节点在左边的连续排列，空位都在右边。<br><img src="https://upload-images.jianshu.io/upload_images/10104523-a0740911374eb600.png?imageMogr2/auto-orient/strip%7CimageView2/2/w/692/format/webp" alt="完全二叉树"><br>图片来源(<a href="https://www.jianshu.com/p/a47d6ed886c8" target="_blank" rel="noopener">https://www.jianshu.com/p/a47d6ed886c8</a>)</p>
<p>那么最大树呢<br>就是一个特殊的完全二叉树，根节点最大，然后左子树和右子树都小于根节点<br>最小数就是根节点最小，左子树和右子树都大于节点的值</p>
<figure class="highlight plain"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br><span class="line">66</span><br><span class="line">67</span><br><span class="line">68</span><br><span class="line">69</span><br><span class="line">70</span><br><span class="line">71</span><br><span class="line">72</span><br><span class="line">73</span><br><span class="line">74</span><br><span class="line">75</span><br><span class="line">76</span><br><span class="line">77</span><br><span class="line">78</span><br><span class="line">79</span><br><span class="line">80</span><br><span class="line">81</span><br><span class="line">82</span><br><span class="line">83</span><br><span class="line">84</span><br><span class="line">85</span><br><span class="line">86</span><br><span class="line">87</span><br><span class="line">88</span><br><span class="line">89</span><br><span class="line">90</span><br><span class="line">91</span><br><span class="line">92</span><br><span class="line">93</span><br><span class="line">94</span><br><span class="line">95</span><br><span class="line">96</span><br><span class="line">97</span><br><span class="line">98</span><br><span class="line">99</span><br><span class="line">100</span><br><span class="line">101</span><br><span class="line">102</span><br><span class="line">103</span><br><span class="line">104</span><br><span class="line">105</span><br><span class="line">106</span><br><span class="line">107</span><br><span class="line">108</span><br><span class="line">109</span><br><span class="line">110</span><br><span class="line">111</span><br><span class="line">112</span><br><span class="line">113</span><br><span class="line">114</span><br><span class="line">115</span><br><span class="line">116</span><br><span class="line">117</span><br><span class="line">118</span><br><span class="line">119</span><br><span class="line">120</span><br><span class="line">121</span><br><span class="line">122</span><br><span class="line">123</span><br><span class="line">124</span><br><span class="line">125</span><br><span class="line">126</span><br><span class="line">127</span><br><span class="line">128</span><br></pre></td><td class="code"><pre><span class="line">public class MaxHeap&lt;E extends Comparable&lt;E&gt;&gt; &#123;</span><br><span class="line">    private Array&lt;E&gt; data;</span><br><span class="line"></span><br><span class="line">    public MaxHeap(int capacity)&#123;</span><br><span class="line">        data = new Array&lt;&gt;(capacity);</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    public MaxHeap()&#123;</span><br><span class="line">        data = new Array&lt;&gt;();</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    /**</span><br><span class="line">     * 返回堆中的元素个数</span><br><span class="line">     * @return</span><br><span class="line">     */</span><br><span class="line">    public int size()&#123;</span><br><span class="line">        return data.getSize();</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    /**</span><br><span class="line">     *返回一个布尔值, 表示堆中是否为空</span><br><span class="line">     * @return</span><br><span class="line">     */</span><br><span class="line">    public boolean isEmpty()&#123;</span><br><span class="line">        return data.isEmpty();</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    /**</span><br><span class="line">     * 返回完全二叉树的中，一个索引所表示元素的父节点</span><br><span class="line">     * @param index</span><br><span class="line">     * @return</span><br><span class="line">     */</span><br><span class="line">    private int parent(int index)&#123;</span><br><span class="line">        if (index==0)&#123;</span><br><span class="line">            throw new IllegalArgumentException();</span><br><span class="line">        &#125;</span><br><span class="line">        return (index-1)/2;</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    /**</span><br><span class="line">     *  返回完全二叉树的数组表示中，一个索引所表示的元素的左孩子节点的索引</span><br><span class="line">     * @param index</span><br><span class="line">     * @return</span><br><span class="line">     */</span><br><span class="line">    private int leftChild(int index)&#123;</span><br><span class="line">        return index * 2 + 1;</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    /**</span><br><span class="line">     * 返回完全二叉树的数组表示中，一个索引所表示的元素的右孩子节点的索引</span><br><span class="line">     * @param index</span><br><span class="line">     * @return</span><br><span class="line">     */</span><br><span class="line">    private int rightChild(int index)&#123;</span><br><span class="line">        return index * 2 + 2;</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    /**</span><br><span class="line">     * 向堆中添加元素</span><br><span class="line">     * @param e</span><br><span class="line">     */</span><br><span class="line">    public void add(E e)&#123;</span><br><span class="line">        data.add(e);</span><br><span class="line">        siftUp(data.getSize()-1);</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    /**</span><br><span class="line">     * 上浮元素</span><br><span class="line">     * 向数组的最后一个位置添加元素，然后查看添加的元素是否大于它的父节点，</span><br><span class="line">     * 如果大于父节点，就要把这个元素与父节点上浮，即与父节点进行位置交换</span><br><span class="line">     * @param i</span><br><span class="line">     */</span><br><span class="line">    private void siftUp(int i) &#123;</span><br><span class="line">        while (i&gt;0&amp;&amp;data.get(parent(i)).compareTo(data.get(i))&lt;0)&#123;</span><br><span class="line">                data.swap(i,parent(i));</span><br><span class="line">                i=parent(i);</span><br><span class="line">        &#125;</span><br><span class="line">    &#125;</span><br><span class="line">    public E findMax()&#123;</span><br><span class="line">        if (data.isEmpty())&#123;</span><br><span class="line">            throw new IllegalArgumentException();</span><br><span class="line">        &#125;</span><br><span class="line">        return data.get(0);</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    public E extractMax()&#123;</span><br><span class="line">        E ret=findMax();</span><br><span class="line">        data.swap(0,data.getSize()-1);</span><br><span class="line">        data.remove(data.getSize()-1);</span><br><span class="line">        siftDown(0);</span><br><span class="line">        return ret;</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    /**</span><br><span class="line">     * 下沉操作</span><br><span class="line">     * 与子节点进行比较，与大的子节点进行位置的交换</span><br><span class="line">     * @param i</span><br><span class="line">     */</span><br><span class="line">    private void siftDown(int i) &#123;</span><br><span class="line">        while (leftChild(i)&lt;data.getSize())&#123;</span><br><span class="line"></span><br><span class="line">            int leftChild = leftChild(i);</span><br><span class="line">            if (leftChild+1&lt;data.getSize()&amp;&amp;data.get(leftChild+1).compareTo(data.get(leftChild))&gt;0)&#123;</span><br><span class="line">                leftChild=rightChild(i);</span><br><span class="line">            &#125;</span><br><span class="line">            if (data.get(i).compareTo(data.get(leftChild))&gt;=0)&#123;</span><br><span class="line">                break;</span><br><span class="line">            &#125;</span><br><span class="line">            data.swap(i,leftChild);</span><br><span class="line">            i=leftChild;</span><br><span class="line"></span><br><span class="line">        &#125;</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    /**</span><br><span class="line">     * 将堆中的最大元素替换</span><br><span class="line">     * @param e</span><br><span class="line">     * @return</span><br><span class="line">     */</span><br><span class="line">    public E replaceMax(E e)&#123;</span><br><span class="line">        E max = findMax();</span><br><span class="line">        data.set(0,e);</span><br><span class="line">        siftDown(0);</span><br><span class="line">        return max;</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line"></span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>

      
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